01 - Whisk together flour, baking powder, and salt in a medium bowl. Set aside for later use.
02 - Beat butter and granulated sugar in a large bowl until light and fluffy, approximately 2-3 minutes.
03 - Add the egg and vanilla extract to the butter mixture, mixing until fully combined.
04 - Gradually add dry ingredients to wet mixture, mixing just until dough forms and no flour streaks remain.
05 - Divide dough in half, shape into flat discs, wrap tightly in plastic wrap, and refrigerate for 30 minutes.
06 - Preheat oven to 350°F and line baking sheets with parchment paper.
07 - On lightly floured surface, roll one dough disc at a time to 1/4-inch thickness. Cut out star or round shapes with cookie cutters.
08 - Arrange cutouts on prepared baking sheets 1 inch apart. Bake for 9-11 minutes until edges are lightly golden.
09 - Let cookies rest on baking sheet for 5 minutes, then transfer to wire rack to cool entirely before icing.
10 - Whisk powdered sugar, 2 tablespoons milk, corn syrup, and vanilla until smooth. Adjust consistency with additional milk if needed.
11 - Divide icing between two bowls. Tint one deep blue and the other black. Gently swirl colors together in a shallow dish.
12 - Dip cooled cookies face-down into marbled icing. Immediately sprinkle with edible stars. Allow icing to set for at least 30 minutes.